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THE FLORIDA STATE UNIVERSITY
COLLEGE OF ENGINEERING
Analysis, Modeling and Simulation of Optimal Power Tracking of
Multiple-Modules of Paralleled Solar Cell Systems
By
Adedamola Omole
A Thesis submitted to the Department of Electrical Engineering
in partial fulfillment of the requirements for the degree of
Master of Science
Degree Awarded:
Fall Semester, 2006
The members of the Committee approve the thesis of Adedamola Omole defended on 07/18/2006.
_____________________ Jie J. Chang Professor Directing Thesis _____________________ Simon Y. Foo
Committee Member _____________________ Rodney G. Roberts Committee Member
Approved:
______________________________________________________________ L. J. Tung, Interim Chair, Department of Electrical and Computer Engineering
______________________________________________________________ C. J. Chen, Dean, College of Engineering
The Office of Graduate Studies has verified and approved the above named committee members.
ii
ACKNOWLEDGMENTS
I would like to take this opportunity to thank my supervisor Dr. Jie Chang for his
valuable guidance and support throughout my graduate program. I would like to thank
my committee members, Dr. Simon Foo and Dr. Rodney Roberts, for their generous
advice and interest.
I would also like to thank the academic and administrative staff in the Department of
Electrical and Computer Engineering and the Center for Advanced Power Systems
(CAPS).
Finally, I would like to thank my family and friends for their support throughout my
graduate school experience.
iii
TABLE OF CONTENTS List of Figures ....................................................................................................vi
List of Tables ...................................................................................................viii
Abstract .............................................................................................................. ix
1. Introduction............................................................................................ 1
1.1 Objectives...................................................................................................... 1
1.2 Motivation..................................................................................................... 2
1.3 Technology Overview................................................................................... 2
1.4 Thesis Organization ...................................................................................... 3
2. Multi-Source Renewable Distributed Energy Generation..................... 5
2.1 Block Diagram of New MRDEG System..................................................... 5
2.2 Photovoltaic Subsystem ................................................................................ 6
2.2.1 Solar Cell Characteristics..................................................................................6
2.2.2 Solar I-V Characteristics...................................................................................7
2.3 Charge Application and MPPT Controllers................................................ 13
2.4 Fuel Cells .................................................................................................... 15
2.4 Energy Storage Devices .............................................................................. 16
3. Analysis and Modeling of MRDEG System and MPPT Circuit......... 17
3.1 System Architecture & Description ............................................................ 17
3.2 Modeling of Key Components and Subsystems ......................................... 18
3.2.1 Solar Cell Math Model....................................................................................22
3.2.2 Solar Cell Circuit Model.................................................................................24
3.3 MPPT Requirement and Circuit Description.............................................. 28
3.3.1 MPPT System Analysis...................................................................................31
3.3.2 Design of a MPPT System..............................................................................34
3.3.3 MPPT Circuit Model in PSpice ......................................................................36
iv
4. Discussion of Practical Circuit Elements ............................................ 40
4.1 Component Selection .................................................................................. 40
4.2 Voltage Sensing .......................................................................................... 42
4.3 Current Sensing........................................................................................... 43
4.4 Testing and Verification.............................................................................. 43
4.4.1 Validation of PV Model ..................................................................................43
4.4.2 Experimental Data ..........................................................................................46
5. Validation of MPPT Circuit Operation and Optimization .................. 49
5.1 Validation of MPPT Circuit Modeling and Operation ............................... 49
5.2 Control and Optimization using Microcontroller ....................................... 54
5.3 Feedback Control using Microcontroller .................................................... 54
5.4 Application of Artificial Neural Networks ................................................. 57
5.4.1 Back-propagation ..........................................................................................57
6. Conclusion and future work................................................................. 60
6.1 Conclusion .................................................................................................. 60
6.2 Further Work............................................................................................... 61
Appendix.................................................................................................. 62
References................................................................................................ 80
Biographical Sketch................................................................................. 83
v
LIST OF FIGURES 2.1: Block diagram of proposed MRDEG system .........................................................5
2.2: Typical I-V characteristic of a solar cell in steady-state operation.........................8
2.3: Typical solar cell I-V characteristic showing the effect of irradiance..................10
2.4: Typical solar cell I-V characteristic showing the effect of temperature...............11
2.5: Illustration of maximum power point ...................................................................12
3.1: Block diagram showing optimal layout of MRDEG system ................................17
3.2: Simplified equivalent circuit of solar cell............................................................19
3.3: Equivalent circuit of solar cell showing external resistances ...............................20
3.4: Electrical characteristics of Sharp NE-80EJEA solar cell ....................................21
3.5: I-V characteristic curve of Sharp NE-80EJEA solar cell .....................................22
3.6: PSpice circuit model of solar cell .........................................................................25
3.7: I-V characteristic for a single solar cell ................................................................26
3.8: I-V characteristic of solar module consisting 36 individual solar cells...............27
3.9: I-V characteristic and output power for the Sharp NE-80EJEA solar cell ...........28
3.10: Basic circuit of a buck converter ........................................................................30
3.11: Waveform of inductor current ............................................................................32
3.12: Waveform of the current through the capacitor..................................................33
3.13: PSpice circuit schematic of error amplifier ........................................................37
3.14: PSpice circuit schematic of PWM ......................................................................38
3.15: Control signal from error amplifier voltage and the PWM output .....................39
3.16: Schematic of two-stage MPPT in PSpice ...........................................................39
4.1: I-V characteristic at 600, 800, and 1000 W/m2 irradiation level ..........................44
4.2: I-V characteristic at 20, 25, 40, and 55 ºC operating temperature........................44
4.3: Output power at 600, 800, and 1000 W/m2 irradiation level................................45
4.4: Output power at 20, 25, 40, and 55 ºC operating temperature..............................46
4.5: Sharp NE-80EJEA solar module used in experiment.....................................................47
5.1: 1st stage of MPPT operating at 17.3V with PV output at 21V..............................49
5.2: 1st stage of MPPT operating at 17.3V with PV output at 20V..............................50
5.3: 1st stage of MPPT operating at 17.3V with PV output at 18V..............................50
5.4: 1st stage of MPPT operating at 15.9V with PV output at 16V..............................51
vi
5.5: 2nd stage of MPPT with PV output at 17.3V and MPPT output at 12V ...............52
5.6: MPPT output voltage with pulsed load added between 1.5ms and 2.5ms............53
5.7: MPPT output voltage with pulsed load added between 1.5ms and 2.5ms............53
5.8: Flowchart of the power-feedback control algorithm.......................................................56
5.9: Structure of back-propagation neural network for maximum power tracking ..............58
A-1: MPPT Circuit PSpice Schematic.....................................................................................62
A-2: Experimental setup for solar module under indoor conditions......................................63
A-3: Sharp NE-80EJEA Solar Cell Data Sheet ......................................................................64
A-4: IdaTech FCS 1200 Fuel Cell Data Sheet........................................................................65
A-5: Maxwell BOOSTCAP Ultracapacitor Data Sheet.........................................................66
B-1: Microchip PIC16F873 Microcontroller Data Sheet.......................................................68
C-1: Intersil IRF150 Power MOSFET Data Sheet .................................................................71
D-1: Fairchild Semiconductor MBR0520L Schottky Diode Data Sheet..............................76
E-1: LEM LA-10PB Current Sensor Data Sheet....................................................................78
vii
LIST OF TABLES 4.1: Solar module measurements under outdoor conditions..................................................47
4.2: Solar module measurements under indoor conditions ....................................................48
viii
ABSTRACT Distributed and renewable energy generation (DG) offers great potential in meeting
future global energy requirements. Distributed generation consists of small to medium
size generators cited close to the customer and spread across a power system. The
production of power from renewable energies will lead to a significant reduction in the
rate of environmental pollution in comparison with the production by fossil fuels, thus
gaining renewed attention due to advances in technology, environmental concerns and a
growing energy demand. Photovoltaic systems in particular have great potential when
compared to other renewable energies. The goals of this thesis are to perform a
systematic analysis, modeling and evaluation of the key subsystems or components of a
multiple-source renewable energy generation system and to develop an optimal tracking
and control strategy. It is desirable to achieve maximum power output at a minimum cost
under various operating conditions.
ix
CHAPTER 1
Introduction
1.1 Objectives
The main challenge in replacing legacy systems with newer more environmentally
friendly alternatives is how to capture the maximum energy and deliver the maximum
power at a minimum cost for a given load. A combination of two or more types of energy
sources might offer the best chance of optimizing power generation by varying the
contribution from each energy source depending on the load demand. The goal is to
develop and optimize maximum power tracking and control of a future Multi-Source
Renewable Distributed Energy Generation (MRDEG) system.
At a subsystem level, solar power is a renewable energy source that might one day soon
replace fossil fuel dependent energy sources. However, for that to happen, solar power
cost per kilowatt-hour has to be competitive with fossil fuel energy sources. Currently,
solar panels are not very efficient with only about 12 ~ 20% efficiency in their ability to
convert sunlight to electrical power. The efficiency can drop further due to other factors
such as solar panel temperature and load conditions. In order to maximize the power
derived from the solar panel it is important to operate the panel at its optimal power
point. To achieve this, a type of charge controller called a Maximum Power Point Tracker
will be designed and implemented.
A solar cell is a non-linear power source and its output power depends on the terminal
operating voltage. The Maximum Power Point Tracker (MPPT) compensates for the
varying voltage vs. current characteristics of the solar cell. The MPPT tracks the output
voltage and current from the solar cell and determines the operating point that will deliver
the most power. The proposed MPPT must be able to accurately track the constantly-
varying operating point where the maximum power is delivered in order to increase the
efficiency of the solar cell.
1
1.2 Motivation
The finite global supply of recoverable fossil fuels implies that at some point in the
future, alternative sources of energy will become the primary source of energy to meet
global demand. Solar and fuel cells represent promising alternatives that will likely
initially supplement fossil fuel based energy supply, and eventually replace the fossil fuel
energy sources as the availability of the latter declines. There is therefore a need to
systematically analyze and understand how solar and fuel cells operate together as an
optimal system.
When compared to fossil fuels, solar and fuel cells are relatively untapped sources of
energy, thus there still remains a lot of work to be done to make solar and fuel cells as
efficient and reliable as possible. One approach to understanding and improving solar and
fuel cell efficiency is digital modeling and simulation. After successfully modeling and
simulating solar and fuel cells, it is possible to develop methods to optimizing the system
operation. The main objective of this research is to first model and simulate the solar cell
subsystem, then optimize the combined system operation based on both solar and fuel
cells to make it as efficient as possible, with a focus on the given solar subsystem.
1.3 Technology Overview
The primary source of fuel for a majority of current power systems are fossil fuels such
as crude oil and coal. These non-renewable forms of energy on earth are ultimately finite
sources of energy. Also burning of oil and coal in the process of conversion to electrical
power can be quite harmful to the environment. Over the past decades there has been a
lot of interest in alternative sources of energy and several approaches have been
suggested to replacing existing energy sources. Renewable energy sources like solar and
wind have shown promise as possible cost efficient alternatives to fossil fuels.
2
As the world energy supplies continue to tighten due to rapid global economic growth,
the scramble for limited available energy resources is fueling a rapid increase in the price
of crude oil and natural gas, the primary sources of energy around the world. The growth
in demand and the attendant increase in price have promoted the development of
alternative energy technologies. Distributed power generation based on renewable energy
is one of such alternative methods. These alternative energy technologies are now being
deployed to meet the world energy demand.
The bulk of electric power used in the world today comes from large central station
power plants, most of which utilize fossil fuel combustion to produce steam for driving
steam turbine generators. The existing large central generating units are not very efficient
as they covert less than 40% of the energy in their fuel to useful electric power [1]. In
comparison, small fuel cells and microturbines suitable for distributed generation have
been shown to have efficiency up to 40% [1]. While these higher efficiency claims are
not irrefutable, there seems to be little doubt that modern distributed generation units can
achieve efficiencies equal to or better than existing central station power plants.
The distributed power generation includes the application of small to medium size
generators, generally less than 15MW, scattered across a power system to supply
electrical power needed by customers. When generating stations are located far away
from the consumer, power has to be transmitted over long distances and there are
significant amounts of power losses as a result of transmission and distribution. By
locating generating stations close to consumers, distributed generation provides
advantages in efficiency and flexibility over traditional large-scale, capital-intensive
central-station power plants.
1.4 Thesis Organization The thesis consists of six chapters, with the first chapter highlighting current
opportunities and challenges to renewable energy generation and distribution. The
motivation for conducting this research is discussed as well as the expected outcome. The
3
first chapter also gives an overview of some current technologies and compares the
possible advantages of one technology over the other.
Chapter 2 will provide a description of the proposed system and review the components
of the system. It will include a literature review on the photovoltaic subsystem, the solar
cell characteristics and cell operation. Charge application and MPPT controllers will also
be reviewed while the selected fuel cells and energy storage devices will be discussed.
Chapter 3 will focus on the analysis and modeling of the system and subsystems.
Mathematical and circuit models of the system will be established based on optimal
system architecture. The solar module will be modeled and simulated in PSpice. The
MPPT requirement will be determined and a design proposed.
Chapter 4 will include the discussion of the practical circuit elements and the testing and
verification of the MPPT model. Here the photovoltaic (PV) model will be validated
using the manufacturer supplied data. This chapter will also present some experimental
data which will be used confirm the theory on solar cell properties.
In chapter 5, the MPPT circuit model and operation will be validated. Control and
optimization methods for the MPPT will be highlighted. The use of microcontrollers and
artificial neural networks in controlling the MPPT operation will also be discussed. The
final chapter concludes the thesis with a look on the future development of this work. The
references and appendix will be attached at the end of the thesis.
4
CHAPTER 2
Multi-Source Renewable Distributed Energy Generation
2.1 Block Diagram of New MRDEG System
For the future Multi-Source Renewable Distributed Energy Generation system being
considered, multiple solar power subsystems based on photovoltaic cell (PVC) arrays will
be operated in parallel connection with fuel-cell arrays and high-density energy storage
components, including super-capacitors. A block diagram of the proposed MRDEG
system is shown in Fig 2.1. In order to achieve maximum energy capture and maximum
power output, the photovoltaic cells should be operated at certain optimal operating
points. The overall power captured by the PVC panels, and the DC or AC output power is
a function of the system’s operating points such as the voltages and currents of different
incoming sources to the energy storage capacitors.
Fig 2.1: Block diagram of proposed MRDEG system
5
2.2 Photovoltaic Subsystem
A photovoltaic (PV) system consists of solar panels that generate electricity by the direct
conversion of the sun’s energy into electricity. The solar panels consist mainly of
semiconductor material, with Silicon being the most commonly used. The components of
a PV system are the solar cells connected in a suitable form and the electronic devices
that interface the storage elements and the AC or DC loads.
One of the major tasks in controlling photovoltaic cells for power generation is
improving cell efficiency and maximizing energy extraction. This requires I-V (current-
to-voltage) measurements to characterize performance and determine the load impedance
that best matches the cell’s source impedance. The best match can then be determined on
a point on the I-V curve of the solar cell.
2.2.1 Solar Cell Characteristics
Solar cells consist of a p-n junction fabricated in a thin layer of semiconductor. The
semiconductor electros can be located in either the valence band or conduction band.
Initially, all the electrons in the semiconductor fill up the valence band but when sunlight
hits the semiconductor, some electrons acquire enough energy to move from the valence
band to the conduction band [2]. The electrons in the conduction band then begin to move
freely creating electricity. The electron leaving the valence band leaves a positively
charged hole behind and now that the valence band is no longer full, it aids the current
flow. Most solar cells are doped to reduce the energy required for the electron to move
from the valence band to the conduction band [3].
The amount of energy from sunlight, called photons, that is absorbed by a solar cell
determines its efficiency. A photon can be reflected, absorbed or it can pass through a
semiconductor [4]. Since only the photons that are absorbed contribute to the electrical
energy, it is important to reduce the percentage of photons that pass through and that are
6
reflected. An anti-reflective coating is usually applied to the surface of the solar cell to
decrease the number of photons that are reflected. This reduces the percentage of photons
that are reflected but some photons are still able to pass right through the semiconductor
material.
The photons in sunlight have a wide range of wavelengths, and some photons at certain
wavelengths are able to pass through the semiconductor material. If a photon has energy
lower than the band gap energy of the semiconductor, the photon is unable to create an
electron-hole pair and the semiconductor will not absorb the photon [4]. On the other
hand, if a photon has more energy than the band gap of the semiconductor, the photon is
absorbed by the valence band electron and any excess energy is emitted as a form of heat
while the electron settles down in the conduction band. To reduce the percentage of
photons that pass through, some semiconductors are manufactured with several layers,
each having a different band gap to maximize the amount of photons that are absorbed.
There are several approaches to manufacturing solar cells, including the kind of
semiconductor used and the crystal structure employed, with each different factor
affecting the efficiency and cost of the cell. Other external factors such as the ambient
weather conditions like temperature, illumination, shading, etc also affect the solar
panel’s output. The aim is to design a system that will extract the most possible power
regardless of ambient weather conditions or solar cell efficiency.
2.2.2 Solar I-V Characteristics
The current-to-voltage characteristic of a solar cell is non-linear, which makes it difficult
to determine the maximum power point. It is straightforward to determine the maximum
power point on a linear curve as maximum power is transferred at the midpoint of the
current-voltage characteristic. A typical I-V characteristic of a solar cell is shown in
Fig. 2.2.
7
Fig 2.2: Typical I-V characteristic of a solar cell in steady-state operation
For a solar cell, the non-linear relationship means the maximum power point has to be
determined by calculating the product of the voltage and output current. In order to
extract maximum power from the solar cell, the solar cell must always be operated at or
very close to where the product of the voltage and output current is the highest. This
point is referred to as the maximum power point (MPP), and it is located around the
‘bend’ or ‘knee’ of the I-V characteristic.
The operating characteristic of a solar cell consists of two regions: the current source
region, and the voltage source region. In the current source region, the internal impedance
of the solar cell is high and this region is located on the left side of the current-voltage
curve. The voltage source region, where the internal impedance is low, is located on the
right side of the current-voltage curve. As can be observed from the characteristic curve,
in the current source region, the output current remains almost constant as the terminal
voltage changes and in the voltage source region, the terminal voltage varies only
minimally over a wide range of output current.
According to the maximum power transfer theory, the power delivered to the load is
maximum when the source internal impedance matches the load impedance [5]. For the
system to operate at or close to the MPP of the solar panel, the impedance seen from the
input of the MPPT needs to match the internal impedance of the solar panel. Since the
impedance seen by the MPPT is a function of voltage (V = I * R), the main function of
8
the MPPT is to adjust the solar panel output voltage to a value at which the panel supplies
the maximum energy to the load. However, maintaining the operating point at the
maximum power point can be quite challenging as constantly changing ambient
conditions such as irradiance and temperature will vary the maximum operating point.
Hence, there is a need to constantly track the power curve and keep the solar panel
operating voltage at the point where the most power is extracted.
Irradiance is a characteristic related to the amount of sun energy reaching the ground, and
under ideal conditions it is measured as 1000 W/m2 at the equator. The sun energy around
the earth is highest around the equator when the sun is directly overhead. Some important
magnitudes related to irradiance include the spectral irradiance, irradiance, and radiation.
Spectral irradiance is the power received by a unit surface area at a particular wavelength,
while irradiance is the integral of the spectral irradiance extended to all wavelengths of
interest. Radiation is the time integral of the irradiance extended over a given period of
time.
In designing PV systems, the main concern is the radiation received from the sun at a
particular location at a given inclination angle and orientation and for long periods of
time. Since solar radiation is the energy resource of the solar panel, the output of the
panel is significantly affected by changing irradiance. The I-V characteristic of a solar
cell including the effects of irradiance is shown in Fig. 2.3.
The irradiance at any location is strongly dependent on the orientation and inclination
angles of the solar panel. Orientation is usually measured relative to the south in northern
latitudes while it is measured relative to the north in southern latitudes. On the other
hand, the inclination angle is measured relative to the horizontal. Using these two
parameters, the irradiation at any location can be determined. The irradiance information
for many sites worldwide is widely available on the internet.
9
Fig 2.3: Typical solar cell I-V characteristic showing effect of irradiance
As can be observed from Fig. 2.3, the output power is directly proportional to the
irradiance. As such, a smaller irradiance will result in reduced power output from the
solar panel. However, it is also observed that only the output current is affected by the
irradiance. This makes sense since by the principle of operation of the solar cell the
generated current is proportional to the flux of photons. When the irradiance or light
intensity is low, the flux of photon is less than when the sun is bright and the light
intensity is high, thus more current is generated as the light intensity increases. The
change in voltage is minimal with varying irradiance and for most practical application,
the change is considered negligible.
Although irradiance is an important factor in determining the I-V characteristic of a solar
panel, it is not the only factor. Temperature also plays an important role in predicting the
I-V characteristic, and the effects of both factors have to be considered when designing a
PV system. Whereas the irradiance mainly affects the output current, the temperature
mainly affects the terminal voltage. A plot of I-V characteristic with varying temperature
is shown below.
10
Fig 2.4: Typical solar cell I-V characteristic showing effect of temperature
It is observed from Fig. 2.4 that the terminal voltage increases with decreasing
temperature. This is somewhat surprising as one would typically expect the solar panel to
operate more efficiently as temperature increases. However, one of the reasons the solar
panel operates more efficiently with decreasing temperature is due to the electron and
hole mobility of the semiconductor material. As temperature increases, the electron and
hole mobility in the semiconductor material decreases significantly [6]. The electron
mobility for Silicon at 25º C is about 1700cm2/volt-sec and will decrease to about a
fourth of this value as temperature increases to 225º C, and likewise the hole mobility
decreases from about 600cm2/volt-sec at 25º C to 200cm2/volt-sec as temperature
increases to 225º C. While the higher reference temperatures are not realistic operating
conditions for a solar panel, it does show that electron and hole mobility decrease with
increasing temperature.
The band gap energy of semiconductor materials also varies with temperature. An
increase in temperature will cause the band gap energy of the material to increase. With
higher band gap energy, the electrons in the valence band will require more energy from
11
the photons to move to the conduction band. This means that a lot more photons will not
have sufficient energy to be absorbed by the electrons in the valence band resulting in
fewer electrons making it to the conduction band and a less efficient solar cell.
It should be noted here that irradiance and temperature represent only two of the most
significant external factors that affect the efficiency of a solar cell; inclination, location,
time of the year are also factors that affect the efficiency of solar cells. Additional
parameters of a solar cell can be discussed by an illustration of the maximum power point
as shown in Fig. 2.5.
Fig. 2.5: Illustration of maximum power point
The cell’s short circuit current intersects the Y-axis at point B and the open circuit
voltage intersects the X-axis at point C. To achieve maximum energy transfer, systems
powered by solar cells should be designed to transfer energy to the load at point A on the
I-V curve. No energy should be delivered at points B and C, and most of the energy
should be delivered as the operating point approaches point A. In a solar panel array, it is
even more important that load impedance and source impedance are well matched. Once
the cells are matched by their I-V characteristics, they can be grouped into individual
arrays and each array is then made to operate at its maximum energy transfer point.
Majority of solar cells have high capacitance associated with their forward biased p-n
junctions because the charged carriers are much closer together. The unwanted
capacitance increases as the size of the solar cell and junction area increases. The I-V
curve of the solar cell can be determined by taking fast I-V measurements which is done
12
by applying a constant voltage and measuring the resulting current for the device being
tested. However the high capacitance makes it difficult to get fast I-V measurements.
The shape of the I-V curve of the solar cell is governed by the cell’s high Thevenin
equivalent impedance [7]. The short circuit current is determined by the incident light
intensity and it is inversely proportional to the applied voltage. The total circuit voltage
and incident light determine the external circuit current.
2.3 Charge Application and MPPT Controllers
Solar panels are rarely connected directly to a load, but rather are used to charge energy
storage components, such as batteries or ultra-capacitors. In most cases, the battery
charging voltage determines the solar panel operating voltage. The battery charging
voltage is usually not the most efficient operating voltage for the solar cell and therefore
the most power is not being extracted from the solar cell. There also exists a possibility of
overcharging when the solar panel is connected directly to a battery and overcharging can
damage the battery. To avoid these potential problems, a charge controller is inserted
between the solar panel and the battery or ultra-capacitor. The most commonly used type
of charge controllers include basic charge controllers, Pulse Width Modulation (PWM)
charge controllers and Maximum Power Point Tracker (MPPT) charge controllers.
The simplest form of charge controllers is the basic charge controller. These are usually
designed to protect overcharging or undercharging of batteries which can cause damage
to the battery. Continually supplying a charging current to a fully charged battery will
increase the battery voltage causing it to overheat and damage. The basic charge
controller simply monitors the state of charge of the battery to prevent overcharge. This
form of charge controller regulates the voltage supply to the battery and cuts off supply
once the battery reaches it maximum charge state. Overcharging some batteries can lead
to explosions or leaking.
13
On the other hand, undercharging a battery for sustained periods will tend to reduce the
life cycle of the battery. The charge controller monitors the state of charge of the battery
to prevent it from falling below the minimum charge state. Once a battery reaches its
minimum charge state, the charge controller disconnects the battery from any load to
prevent the battery from losing any more charge. The basic charge controllers are usually
operated by a simple switch mechanism to connect and disconnect the battery from the
solar panel or load to prevent overcharging and undercharging.
While the basic charge controller is only able to connect or disconnect the battery from
the solar panel to prevent overcharging, PWM charge controllers are able to regulate the
charging current to the battery in order to optimize the charging time. As the battery
approaches its maximum charge state, the PWM charge controller switches the charging
on and off using pulse width modulation to slowly charge the battery. Slowly charging
the battery as it approaches maximum capacity optimizes the speed and efficiency at
which the battery is charged [8]. Both the basic charge controller and the PWM charge
controller control the charging current going into the battery but do not address the
operating efficiency of the solar panel.
The drawback of both the basic charge controller and the PWM charge controller is that
they operate the solar panel at the battery charging voltage. For a vast majority of solar
panel designs and applications, setting the solar panel voltage to the battery charging
voltage causes the solar panel to operate away from its optimal operating point. Since the
maximum operating point on the I-V curve of the solar panel varies with irradiance and
temperature, operating the solar panel at a fixed point as the basic and PWM charge
controllers do will guarantee that the solar panel will mostly operate away from its
maximum power point.
Maximum Power Point Tracker charge controllers optimize the power output of the solar
cell while also charging the battery to its optimal state. The MPPT constantly tracks the
varying maximum operating point and adjusts the solar panel operating voltage in order
to constantly extract the most available power. The MPPT charge controller maximizes
14
solar cell efficiency while also controlling the charging state of the battery. The MPPT
charge controller is basically a DC-DC converter that accepts a DC input voltage and
outputs a DC voltage higher, lower or the same as the input voltage. This capability of the
converter makes it ideal for converting the solar panel maximum power point voltage to
the load operating voltage. Most MPPT charge controllers are based on either the buck
converter (step-down), boost convert (step-up) or buck-boost converter setup [9].
2.4 Fuel Cells
Fuel cells are electrochemical devices that generate electrical energy by harnessing the
energy produced during a chemical reaction. Fuel cells convert hydrogen and oxygen into
water and in the process generate electricity. There are several different approaches to
designing fuel cells, and they vary by chemistry. However, fuel cells are usually
classified by the type of electrolyte that is used in the chemical process. The proton
exchange membrane fuel cell (PEMFC) is one of the most promising technologies [10].
The fuel cell unit selected for the MRDEG system, the IdaTech FCS1200, is a proton
exchange membrane type of fuel cell. The IdaTech FCS1200 uses a methanol and de-
ionized water mix to generate high purity hydrogen, which is then stripped of electrons to
create the hydrogen ion [11]. The hydrogen ion passes through the PEM and in the
process electricity is generated. The hydrogen ion, stripped electrons and oxygen in air
combine to form water. The fuel cell has a peak power of 2000W for sixty seconds at DC
and it is able to continually output 1000W.
Additional specification about the IdaTech FCS1200 fuel cell including the
manufacturer’s Data Sheet is provided in the appendix.
15
2.4 Energy Storage Devices
Ultra-capacitors are used in parallel with battery banks to store the energy produced by
the PV module. The ultra-capacitor is an electrochemical capacitor that is able to store a
very large amount of energy relative to its size and weight. The ultra-capacitor is used as
the main energy storage element since it provides much faster charge and discharge times
and it also has a much longer life cycle than batteries. The high-energy battery bank is
included in the system for reduced cost.
The ultra-capacitor and battery operating voltage is assumed to be 12V for our system,
which is typical for many DC applications. The PV module initially charges the ultra-
capacitor to the operating voltage and once the ultra-capacitor is fully charged, the battery
bank begins to charge. A blocking diode is placed between the ultra-capacitor and the
battery in order to prevent damage to the battery that might arise due to excessive
currents between the two components. The blocking diode ensures that the current flows
in only one direction: from the ultra-capacitor to the battery.
The Maxwell BOOSTCAP ultra-capacitor is selected for the project and additional
specification about the ultra-capacitor is provided in the appendix.
16
CHAPTER 3
Analysis and Modeling of MRDEG System and MPPT Circuit
3.1 System Architecture and Description
Solar and fuel cells will be the main energy source for a future Multi-Source Renewable
Distributed Energy Generation (MRDEG) System. Multiple solar photovoltaic cell (PVC)
arrays will be operated as subsystems in parallel connection with fuel cell arrays and
high-density energy storage components, including super-capacitors. All the components
of the proposed MRDEG system are arranged in such a way as to achieve maximum
power output at a minimum cost under various operating condition.
This new system also consists of a multi-function power converter supporting multi-
source renewable distributed energy units (MSREU). The PV modules act as the primary
source of energy and consist of single solar panels arranged in series and parallel to
match the voltage and power output requirement. The fuel cell modules act as backup in
periods of no sunlight and when the energy storage devices are discharged. A block
diagram of the optimal architecture for the system is shown in Fig. 3.1 below.
Fig 3.1: Block diagram showing optimal layout of MRDEG system
17
One of the core technologies of the MRDEG system is the advanced multi-function
power converter that also provides an integrated system control to manage the power
flow between supply components and AC or DC load.
Ultra-capacitors are used in parallel with batteries to store the energy produced by the PV
modules. Ultra-capacitors are used because they provide much faster charge and
discharge times and also a much longer life cycle than batteries [12]. The PV modules
directly feed the DC-DC buck converter. A blocking diode is placed between the ultra-
capacitor and the battery to prevent excessive currents between the two components. The
buck converter is operated by a feedback PWM controller that monitors the incoming
voltage and current levels and controls the buck converter accordingly [13]. The ultra-
capacitors and batteries then feed AC and DC loads through the power converter during
sunlight hours and at nighttime.
3.2 Modeling of Key Components and Subsystems
To properly model a solar cell and subsystems, it is important to understand how solar
cells operate and how a simple PSpice model can be generated. Solar cells are primarily
made of semiconductor material that when exposed to light induce a process of photon
reflection and absorption, generation of free carriers and lastly charge separation, which
creates an electric field. The semiconductor properties determine how effectively this
process occurs. Some of the most important properties include the absorption coefficient,
the reflectance of the semiconductor surface, drift-diffusion parameters and surface
recombination velocities.
The absorption coefficient depends on the value of the bandgap of the semiconductor
material and the nature of the bandgap. Absorption coefficient values for the most
commonly used semiconductor materials are widely available. The reflectance of the
semiconductor surface depends on the surface finishing, particularly the shape and
18
antireflection coating. Drift-diffusion parameters control the migration of charge towards
the collecting junction; the parameters are carrier lifetimes, and mobilities for electron
and holes. It is also important to know the surface recombination velocities at the surface
of the solar cell where minority carriers recombine. These factors effectively determine
how much of the sun’s energy a solar cell can capture and successfully convert to
electrical energy.
For practical power applications, the voltage produced by one solar cell is usually not
sufficient to power most equipment. An array of between 20 to 80 solar cells connected
in series to form a “Solar Module” is usually necessary to provide the required voltage.
Solar cell manufacturers can provide some key parameters of a solar module in their Data
Sheet. The output power is given in Wp (Watt peak), which means the module was rated
at Standard Test Conditions (STC). The STC are an illumination level of 1000 W/m2
(bright sunshine), a spectrum equivalent to AM 1.5 and 25°C module temperature at the test.
The manufacturer’s data sheet also provides the short circuit current, the current produced
when the output voltage is zero, and the open circuit voltage, the voltage across the output
terminals when there is no current flowing in the cell.
A simplified equivalent circuit of a solar cell consists of a diode and a current source which are
switched in parallel. The photocurrent generated when the sunlight hits the solar panels can be
represented with a current source and the p-n transition area of the solar cell can be represented
with a diode.
Fig 3.2: Simplified equivalent circuit of solar cell
19
The voltage and current relationship of the simplified solar cell can be derived from Kirchoff’s
current law. According to Kirchoff’s current law, all currents entering and leaving a node add
up to zero.
Thus,
C)25at (25.7mV voltageThermal is factor ideal Diode is
current saturation reverse Diode is current Diode is
ntphotocurre theis where
)1.3(1)exp(
°
⎥⎦
⎤⎢⎣
⎡−
⋅⋅−=−=
T
S
D
Ph
TSPhDPh
VmIII
VmVIIIII
This simplified equivalent circuit, however, does not give an accurate representation of the
electrical process at the solar cell. On real solar cells, voltage losses occur at the boundary and
external contacts and leakage currents occur throughout the cell; these losses can be represented
with a series resistance RS and a parallel resistance RP respectively. The equivalent circuit of the
solar cell showing the series and parallel resistance is shown below
Fig 3.3: Equivalent circuit of solar cell showing ext resistances
20
The voltage and current relationship can also be derived from Kirchoff’s current law:
(3.2)
(3.3) 0)1)(exp( =−
⋅+−−
⋅⋅+
⋅−
⋅+==
IR
RIVVm
RIVII
RRIV
RV
I
P
S
T
SSPh
P
S
P
DP
As an example, a practical solar module selected for our lab experimental system is the Sharp
NE-80EJEA solar cell. The solar module is able to output a maximum power of 80W. The
specifications of the solar module and I-V characteristic curves as well as the maximum power
operating curves are supplied by the manufacturer’s data sheet as shown in Fig. 3.4 and Fig.
3.5.
Fig 3.4: Electrical characteristics of Sharp NE-80EJEA solar cell
21
Fig 3.5: I-V characteristic curve of Sharp NE-80EJEA solar cell
3.2.1 Solar Cell Math Model
A math model of the selected PV module will be given in this section. It can be used in the
determination of the voltage and current at which the maximum power is extracted from the
solar cell.
The current through the solar cell can be derived from
phVV
S IeII T −−= )1( (3.4)
Note that this expression is a simplified form of the equation provided earlier as it does not
include the diode ideal factor, essentially ignoring the recombination in the depletion region. The
22
photocurrent, , is assumed to be independent of applied voltage and is the saturation current
of the diode.
phI SI
m
Toc
T
mToc ph m
T
mToc
m
Tph m m m
VVV
VV
VV I P
VV
VVVV
I V I P
−+− − ≈
+−−− ≈ × = 1(
)1ln((
)) 1ln()(
ent is n
(3.5)
he open circuit voltage , is the voltage with zero current and equals
(3.6)
he total power dissip
The short circuit curr the current with o voltage applied and equals
, scI ,
phsc II −=
T , ocV
S
phT
S
phToc I
IV
II
VV ln)1ln( ≈+=
T ated equals
VIeVIIVP phVV
ST −−=×= )1( (3.7)
By taking into account that maximum power occurs when 0=dVdP , it is possible to derive the
maximum voltage point, , and the maximum current point, as
mV mI ,
T
mm VVVIdP
T V
T
mSph
VS e
VIeI
dV+−−== )1(0 (3.8)
At the maximum power point equation can be rewritten as
⎥⎦
⎤⎡ mV⎢⎣+−=
TTocm V
VVV 1ln (3.9)
can be calculated by solving the transcendent equation above provided is known.
mV ocV
)1(0 −−= T
mVV
m eIII (3.10)
ower can be appro
(3.11)
(3.12)
The maximum p ximated by` , mP ,
23
For the Sharp NE-80EJEA solar cell, the following parameters are determined by the
= 17.3 V
manufacturer as:
Vm
= 4.63 A mI
mP ≈ × = 80.01 W mV mI
nother interesting parameter of a solar cell math model is the fill factor (FF). The fill
ola tput p
A
factor is defined as the ratio between the maximum power mP and the scI ocV product; the
conversion efficiency is defined as the ratio between the s r cell ou ower and the
solar power impinging the solar cell surface
scoc
mm
IVIV
FF = (3.13)
in
Scoc
in
mm
PIV
FFP
IV==η (3.14)
or our lab prototype solar cell the fill factor is 0.718.
.2.2 Solar Cell Circuit Model
model of the Sharp NE-80EJEA solar cell is implemented in Pspice. From the electrical
F
3
A
characteristics of the solar cell, it is apparent that the solar cell is a non-linear device. One
approach to handling non-linear circuits in Pspice is to define subcircuits for the main blocks.
Using subcircuits to model the solar cell is particularly helpful when connecting several solar
cells in series or in parallel as required for the application.
24
The Pspice model of the subcircuit of an ideal solar cell is the circuit representation of the
current equation (3.4) of a solar cell. The short circuit current is proportional to the irradiance
that the solar cell receives, and in order to implement this relationship in Pspice, the value of the
short circuit current is assigned to a voltage-controlled current source (known as a G-device in
Pspice). The G-device used is named ‘gsource’ and is given by
GAJ
gsource sc
1000= (3.15)
Where A is the solar cell surface area, is the short-circuit current density under
standard (AM1.5G, 1000 W/m
scJ2, 25 ºC cell temperature), and G is the value of the
irradiance in W/m2. The above equation gives the value of the short circuit current at any
irradiance value , so long as the proportionality between irradiance and short circuit
current holds.
G
The solar cell subcircuit is connected to an external measurement circuit in order to
obtain the I-V characteristic. The external circuit includes a DC bias voltage source
which is swept from 0v to 600mV. A PSpice model of the solar cell is shown below in
Fig. 3.6. The single solar cell is successfully modeled and simulated and the I-V
characteristic is shown in Fig. 3.7.
Fig 3.6: PSpice circuit model of solar cell
25
Fig 3.7: I-V characteristic for a single solar cell
The intersection of the graph with the y-axis gives the value of the short circuit current of
the solar cell, which in this case corresponds to 5.16A. The open circuit voltage for each
cell can also be derived from the I-V plot. The crossing of the I-V curve with the voltage
axis is the open circuit voltage, which corresponds to almost 600mV for each individual
solar cell. According to the specifications supplied in the Manufacturer Data Sheet
(MDS) of the Sharp NE-80EJEA, there are 36 cells connected in series, hence the total
open circuit voltage is 600mV × 36 = 21.6V.
From the equation of the open circuit voltage (3.6), it is observed that the value of the
open circuit voltage depends logarithmically on the ratio. This implies that under
constant temperature the value of the open circuit voltage scales logarithmically with the
short circuit current, but since the short circuit current scales linearly with irradiance, it
means the open circuit voltage is logarithmically dependent on the irradiance. This
important relationship indicates that the effect of irradiance is much larger in the short
circuit current that in the open circuit voltage value.
Sph II /
26
The selected solar module represents 36 identical solar cells connected in series, with the
same irradiance value. The I-V characteristic of the solar module is expected to have the
same short circuit current as a single solar cell while the voltage drop is 36 times the
voltage drop in one solar cell. The I-V characteristic of the solar module is shown below
in Figure 3.8.
Fig 3.8: I-V characteristic of solar module consisting 36 individual solar cells
The output power of the solar cell is the product of the output current delivered to the load and
the voltage across the cell. The power at any point of the I-V characteristic is given by
equation (3.7). There is no power output at the short circuit point where the voltage is zero and
also at the open circuit point where the current is zero. Power is generated between the short
circuit point and the open circuit point on the I-V characteristic. Somewhere on the
characteristic, between the two zero points, there exist a point where the solar cell generates the
most power. The point is called the maximum power point (MPP). A plot of the I-V
characteristic including the output power of our solar cell is shown in Fig. 3.9.
27
Fig 3.9: I-V characteristic and output power for the Sharp NE-80EJEA solar cell
3.3 MPPT Requirements and Circuit Description
The Maximum Power Point Tracker (MPPT), a type of charge controller, is an electronic
system that operates the PV module in a way that allows the module to produce the maximum
power. Without an MPPT charge controller, the operation of a solar module with a
conventional (non-MPPT) charge controller is as follows: for a conventional controller
charging a load, e.g. battery, the solar modules are connected directly to the load. This forces
the modules to operate at the load voltage, say 12V for the battery, but this is typically not the
optimal operating voltage at which the modules are able to produce their maximum power.
For example, the PV module I-V/power characteristic for our prototype solar cell in Fig 3.8
shows that for a solar module connected directly to a battery load, the operating voltage of the
solar module is clamped to the battery charging voltage of VVb 12≤ . By forcing the solar
module to operate at , the power produced is artificially limited to less than
approximately 60W, but the solar module is actually capable of delivering a maximum of 80W.
Hence the solar module is operating 33% less efficiently than if it were able to produce its
maximum power.
VVb 12≤
28
Introducing an MPPT charge controller will allow more power to be produced by the solar
module [13]. First, the operating voltage at which the solar module produces the most power
must be determined. Then a high efficiency DC-DC power converter is used to adjust the solar
module maximum power voltage at the converter input to the battery charging voltage at the
converter output. From the I-V/Power characteristic of our solar module, the maximum power
point is estimated at 17V. The MPPT system is made to operate the solar module at 17V, thus
extracting the full 80W, regardless of the load voltage. Assuming an ideal system, the battery
charging current would now be a ratio of the module operating voltage and the battery charging
voltage multiplied by module operating current ( Α=Α×÷ 66.67.412VV17 ). This represents
a charge current increase of about 1.5A or 29% that would have been wasted using a
conventional charge controller. This gain will be somewhat smaller under normal operating
conditions due to non-ideal power losses associated with the system.
Apart from improving charging efficiency for battery loads and other energy storage elements,
MPPT charge controllers are particularly useful in applications where the life of the load can be
strongly reduced when forced to work in extreme conditions [14]. A solar module’s operating
condition may vary as the weather outside becomes hot or due to partial shading of the solar
panels. The MPPT ensures that applications such as DC motor water pumps are not forced to
work outside their safe operating area (SOA).
The main component of the MPPT in this example system is the DC-DC buck converter that
steps down the solar panel output voltage to the desired load voltage. To ensure that the solar
module operates at the maximum operating point, the input impedance of the DC-DC converter
must be adapted to force the solar module to work at its maximum power point [15].
Depending on the load requirement, other types of DC-DC converters can be employed in the
MPPT design. For example, the boost converter is able to output a higher voltage from a
nominal input voltage; other types of DC-DC converter include the buck-boost converter, CuK
converter and full-bridge converter [16].
The buck converter uses energy storage components such as inductors and capacitors to control
the energy flow from the solar module to the load by continuously opening and closing a
29
switch. The switch is usually an electronic device that operates in two states: in the conduction
mode (on), the output of the solar cell in connected to an inductor while in the cut-off mode
(off), the output of the solar module is disconnected from the inductor. The buck converter also
contains a forward biased diode that provides a return path for the current in the cut-off state.
The basic circuit for the buck converter is shown below in Figure 3.10.
Fig 3.10: Basic circuit of a buck converter
The switch is actually a MOSFET that is controlled by a PWM signal. The switch conducts on
and off to control the voltage level at the inductor. The voltage at the inductor has a rectangular
waveform that is later filtered by the LC combination to produce a quasi-continuous voltage at
the output. The average value of the rectangular waveform can be adjusted to control the length
of the conduction and cut-off states of the switch. The on time of the switch is related to its time
period such that , where D is the duty cycle. In the ON state, current flows from the
module through the inductor causing the inductor to store energy. In this state the diode is in
reverse bias and no current flows through it. In the OFF state, the off time is given by
and the current in the inductor causes the diode to become forward biased. The
diode turns ON and provides a path to maintain the continuity of current through the inductor.
DTton =
TDtoff )1( −=
The duty cycle can be adjusted to set the output voltage of the converter to the desired value.
For an ideal DC-DC converter, the duty cycle is the ratio between the output voltage and the
input voltage, oiio IIVVD == . For our system, the DC-DC converter is used as a DC
power supply, where the input voltage varies with temperature and insolation conditions, but
the output voltage is maintained at a desired value. This allows the duty cycle to be set such that
30
the input voltage to the DC-DC converter is always set at the solar module’s maximum power
point voltage. The duty cycle is set by means of a pulse width modulation (PWM) signal used
to control the MOSFET on and off states.
3.3.1 MPPT System Analysis
The buck converter contains two energy storage elements, the inductor and capacitor. The two
elements result in a second order differential equation for both the inductor current and the
capacitor voltage. The differential equation for the capacitor voltage, in the ON state, is given
by
iCCC VtVdt
tdVRL
dt(t)Vd
LC =++ )()(
2
2
(3.16)
Assuming that the voltage across the load, and thus the capacitor, is constant, then the
differential equation above can be simplified and can be written for the current through the
inductor as
oiL VVdt
tdiL −=
)( (3.17)
If the circuit has been on for some time and is now in steady state, the solution for the current
through the inductor yields
0,)( Loi
L ItL
VVti +
−= (3.18)
Where is the current in the inductor just before the switch is turned on. The inductor
current increases linearly with time and attains it final value, , as
0,LI
LI DTtt on =→
0,Loi
L IDTL
VVI +−
= (3.19)
The difference between the final and initial value of the inductor current is called the
peak-to-peak current ripple Δ , and is given by LI
31
DTL
VVIII oi
LLL−
=−=Δ 0, (3.20)
The current ripple is directly proportional to the duty cycle, D, and inversely proportional
to the inductance, L. Thus, the current ripple can be controlled by the duty cycle or with
proper selection of the inductor.
For the OFF state, the inductor current flows through the diode and the first order
differential equation is given by
0)( V
dttdiL L −= (3.21)
The solution of the differential equation yields
LL ItLVti +
−= 0)( (3.22)
Here is the value of the current in the inductor just as the switch is opened. The
inductor current decreases to its minimum value, , as LI
0,LI TDtt off )1( −=→
LL ITDL
VI +−−= )1(0
0, (3.23)
The equation gives a peak-to-peak current ripple equation
TDL
VIII LLL )1(0
0, −=−=Δ (3.24)
The above equation can be simplified to
io DVV = (3.25)
The waveform of the inductor current is shown below
Fig 3.11: Waveform of inductor current
32
The average current in the inductor is equal to the DC current through the inductor
RV
II ooavgL ==, (3.26)
Using the equation above, the maximum current through the inductor is
TDL
VR
VIII ooLavgLL )1(
22, −+=Δ
+= (3.27)
And the minimum current through the inductor is
TDL
VR
VIII ooLavgL )1(
22,0 −−=Δ
−= (3.28)
Assuming all the components are ideal and there is no power loss, the average power supplied
by the source is equal to the average power delivered to the load [17], that is
(3.29) oiooii IDVIVIV ==
Using the above equation, the average load current may be expressed in terms of the source
current as
(3.30) oi DII =
The difference between the inductor current and the load current is the time-varying current
through the capacitor. The maximum and minimum current through the capacitor are
)32.3()1(
22
)31.3()1(22
0, TDL
VII
TDL
VII
oLC
oLC
−−=Δ
−=
−=Δ
=
The waveform for the current through the capacitor is shown below
Fig 3.12: Waveform of the current through the capacitor
33
The average current through the capacitor is zero. During one-half cycle, the current is charging
the capacitor and the increase in charge is given by
TITIQ L
L Δ=Δ
=Δ81
2221
(3.33)
The increase in capacitor voltage is
ooo VLCf
DTVLC
DCQV 2
2
81
81 −
=−
=Δ
=Δ (3.34)
The capacitor ripple is the ratio of the increase in capacitor voltage to its average value and is
given by
281LCf
DVV
o
o −=
Δ (3.35)
To ensure that the buck converter operates in continuous conduction mode (CCM), i.e. the
minimum current can be zero at the time of switching, a minimum value of the inductor is
determined by
)37.3(
21
21
)36.3(0)1(2
min
min
RfDRTDL
TDLV
RV oo
−=
−=
=−−
3.3.2 Design of a MPPT System
A high frequency DC-DC buck converter consisting of two simple conversion stages is
proposed for the maximum power point tracker. Each stage of the converter will be designed
according to the MPPT system equations. The first stage of the converter, which maintains the
output voltage of the solar module at the maximum power point, has a target output of
approximately 17.3V. Since the actual power delivered by the solar module will vary with
temperature and insolation conditions, it is necessary to initially assume a fixed operating
voltage in determining the parameters of the devices to be used.
34
For our case, an open-circuit voltage of 20V has been selected. This operating voltage is used
to select an initial duty cycle for the MOSFET and also choose appropriate element values.
Once the device parameters have be chosen, the feedback mechanism of the MPPT will
dynamically adjust the duty cycle according to the actual operating condition of the solar
module. Thus, the fist stage of the buck converter has the following properties:
The duty cycle, from equation (3.24), is
865.020
3.17==D
The time period is
sf
T μ3.3033000
11===
The on and off times for the switch are
sTDt
sDTt
off
on
μ
μ
09.4)103.30)(865.01()1(
2.26103.30865.06
6
=×−=−=
=××==−
−
The equivalent resistance is
Ω=== 74.380
3.17 22
PV
R o
The minimum value of the inductor for CCM, from equation (3.37), is
HR
fDL μ65.7)74.3(
000,332865.01
21
min =⎟⎠
⎞⎜⎝
⎛×−
=−
=
Assuming a voltage ripple of 1%, the value of the capacitor is
Ff
VV
L
DC
o
oμ202
000,3301.01065.78865.01
8
126
2=
××××−
=Δ−
= −
Similarly for the second stage of the buck converter, which maintains the output voltage at 12V
regardless of load variations, the properties are as follows:
35
The duty cycle is
694.03.17
12==D
The time period is
sf
T μ3.3033000
11===
The on and off times for the switch are
sTDt
sDTt
off
on
μ
μ
27.9)103.30)(694.01()1(
21103.30694.06
6
=×−=−=
=××==−
−
The equivalent resistance is
Ω=== 8.180
1222
PVR o
The minimum value of the inductor for CCM, from equation (3.37), is
HRfDL μ35.8)8.1(
000,332694.01
21
min =⎟⎠
⎞⎜⎝
⎛×−
=−
=
Assuming a voltage ripple of 1%, the value of the capacitor is
Ff
VV
L
DC
o
oμ420
000,3301.01035.88694.01
8
126
2=
××××−
=Δ−
= −
3.3.3 MPPT Circuit Model in PSpice
The MPPT circuit model consists of two power conversion stages; the first stage matches the
input of the converter to the maximum power point voltage of the solar module while the
second stage matches the output load voltage. Therefore, two different control references are
required to control the length of the conduction and cut-off times for each stage. As with the
solar cell circuit model, the MPPT circuit is implemented in Pspice. Each stage of the power
converter will consist of (i) an error amplifier to measure the difference between the output
36
voltage and the desired reference voltage, and (ii) a PWM generator to control the MOSFET
switch of the converter.
The error amplifier is an essential part of the feedback loop since it is able to adjust the input
voltage to drive the buck converter to the desired output. The error amplifier measures how
close the output voltage is to the desired voltage. The measurement of error is the difference
between the output voltage and the reference voltage, ( )refoErrAmp VVkV −= . In PSpice, the
error amplifier is modeled with an operational amplifier that generates a voltage equal to the
difference between the output voltage and the reference voltage. The error then drives the
PWM circuit. The PSpice circuit diagram of the error amplifier is shown below
Fig 3.13: PSpice circuit schematic of error amplifier
A capacitor is added to model the bandwidth limit of the error amplifier. A low pass RC filter
combination is also included to limit the high frequency gain of the amplifier; this is necessary
to prevent wild ringing or oscillations [18]. Finally, a diode is added to clamp the error voltage
to an appropriate range. The logic behind the error amplifier is as follows: (i) when the
difference between the output voltage and the reference voltage is positive, the duty cycle is
increased; (ii) when the difference is negative, the duty cycle is decrease; while the duty cycle
is maintained when the difference between the output and reference voltage is zero.
37
A pulse width modulation signal is used to drive the MOSFET, which controls the power flow
from the input to the output of the converter. Two main components are used to model the
PWM: a triangle wave and a comparator. Pspice does not have a triangle wave
generator/source, but a triangle wave can be achieved with a square wave generator with long
rise and fall times. The comparator is achieved by the use of an operational amplifier and the
TABLE function in Pspice. As the output of the error amplifier varies between zero and its
maximum value, the PWM output changes from 0% to 100% duty cycle. The output of the
PWM then drives the MOSFET switch. Since there are two stages in the MPPT design, each
stage will require a unique PWM signal. The PSpice circuit diagram of the PWM is shown in
Fig. 3.14 below
Fig 3.14: PSpice circuit schematic of PWM
The MPPT control circuit has implemented and evaluated by digital simulation in Pspice. The
output of the error amplifier and the PWM are shown in Fig. 3.15. The complete schematic of
the MPPT showing both stages of the power conversion is shown in Fig 3.16. For a convenient
collation of the results, the maximum power point of the solar cell is assumed to be 80% of the
open circuit voltage [19], , in our case ocV V17.280.8V6.21 =× . Thus, the solar module is
represented with discrete DC voltage sources ranging from 16V, under unfavorable weather
conditions, to 21.6V, the open circuit voltage.
38
Fig 3.15: Control signal from error amplifier voltage and the PWM output
Fig 3.16: Schematic of two-stage MPPT in PSpice
39
CHAPTER 4
Discussion of Practical Circuit Elements
4.1 Component Selection
There are several factors to be considered when selecting the key devices or components to be
used in the circuit of the maximum point power tracker, but one of the most important is the
power loss associated with each device. Since the objective of the tracker is to deliver
maximum power from the solar module to the load, power losses associated with the tracker
itself should be minimal. The primary parts of the MPPT are simple and readily available
components and they include the MOSFET, diodes, operational amplifiers, inductors,
capacitors and resistors. Each component has some power loss associated with it. A power loss
comparison is used to select the specific type of element that is best suited for the design.
There are three main types of power losses associated with the MOSFET: the first is due to the
small internal resistance when in the conduction state, the second is due to the small internal
capacitance at the gate of the MOSFET, and the third is due to the rise and fall times of the
switch [20]. The on-resistance (rDS) and gate-to-source charge (QGS) constitute a majority of the
loss; the lower the rDS and QGS values, the lower the power loss. The conduction loss due to the
on-resistance of a MOSFET is a function the current passing through it: . RIPon2=
The gate-to-source charge is the amount of charge required to close the MOSFET switch. A
capacitor connected between the gate and the source of the MOSFET stores the charge and
once enough charge has accumulated, the switch is closed allowing current to flow from the
drain to the source. The charge stored in the capacitor dissipates once the switch is closed and
this results in some power loss; the relationship between the amount of charge stored and the
power loss is . This power loss is dependent on the switching frequency. fVQP GSGSS =1
40
The third form of power loss associated with the MOSFET is due to the rise and fall times of
the device. When the MOSFET switches on, the switch is not instantaneous and there is some
delay as the current begins to flow and the voltage drop decreases to zero. Similarly, when the
MOSFET is switched off, the current reduces to zero and the voltage drop increases to its
maximum value. During the delay, as the voltage drop increases or decreases, there is still some
current and as such some power loss: fIVP DSS ×=21
2 . Here, the power loss of is also a
function of frequency. The overall power loss in the MOSFET is the sum of the three types of
power losses. After an evaluation, the IRF150 power MOSFET is selected due to its suitable
ratings for this design.
2SP
The diode is one of the components of the MPPT with the highest power loss. The power loss
is mainly due to the forward voltage drop of the diode, which can be significant for some
diodes. The forward voltage drop is the voltage required before the diode is turned on and
current is allowed to flow. The Schottky diode has the lowest on voltage (0.2 – 0.9V) when
compared to other silicon general purpose and fast recovery diodes (0.7 – 2.5 V). There is a
trade-off between the recovery speed, the breakdown voltage and the forward voltage drop. In
our case, the lower forward voltage drop is preferable to the fast recovery speed and therefore
the Schottky diode is suitable for the design.
Another component whose power loss varies as a function of frequency is the inductor. All
inductors have some internal resistance, and the power loss is due to this resistance. Hence, the
lower the internal resistance of an inductor, the lower the power loss will be. The internal
resistance varies inversely with the wire gauge [21]; i.e. as the wire gauge increases, the internal
resistance decreases. In general, a bigger inductor will have less internal resistance than a
smaller inductor as more current passes through the bigger inductor. The drawback is the size
and cost of the bigger inductor. Therefore, when selecting an appropriate inductor, it is
important to strike a balance between a low internal resistance and the size and cost of a bigger
inductor.
41
The power loss associated with the capacitor is similar to what obtains in the inductor. The
parasitic series resistance causes heat to be dissipated resulting in power loss. When choosing
the appropriate capacitor, a lower equivalent series resistance (ESR) should result in lower
power loss. However, if the ESR is too low, arcing or welding can occur at the contacts,
especially for non-solid state capacitors.
4.2 Voltage Sensing
Voltage measurements are required at several points in the circuit, particularly at the solar
module output, and at the buck converter output. At the PV output, the voltage is measured
with no current flowing to determine the open circuit voltage of the PV module. A fraction
(80%) of the open circuit voltage is then used to determine the maximum power point voltage.
Another point where the voltage measurement is required is the output of the first stage of the
buck converter. The voltage at this point is the maximum power point voltage of the PV
module. This desired MPP voltage is compared to the measured voltage and the difference is
fed into an error amplifier that controls the PWM to achieve the necessary duty cycle needed to
control the MOSFET switch.
The voltage at the output of the first stage of the converter is also the input voltage to the
second stage of the converter. A measurement of the voltage at the output of the second stage
of the buck converter is required to adjust the error amplifier and PWM to control the duty
cycle, which then matches the desired load voltage. These voltage measurements are
continuously collected and used in a dynamic feedback loop to maintain the solar module
output and the load voltage at the desired levels. The voltage measurements can be achieved
with the use of a high-impedance voltage sensing circuit [22].
42
4.3 Current Sensing To measure the current through certain elements in the circuit, a small precision resistance
(0.01Ω) connected in series with the elements can be used. The voltage drop across the resistor
is directly proportional to the current through the element. The current measurements are
necessary to ensure that the current through each element is within the device rating and the
current supplied to the load is within the safe operating area of the load. The current
measurements are particularly important in determining the power loss due to each element. In
PSpice, the measurements are achieved by using the PROBE function of the software.
4.4 Testing and Verification
The circuit models of the solar cell and the maximum point power tracker have been simulated
in PSpice. The solar cell and MPPT models must closely match the actual solar cell and desired
operation of the MPPT so as to be able to accurately predict the performance of the system
under varying atmospheric and load conditions. The circuit model of the solar cell is used to
evaluate the effect of varying irradiation and temperature conditions on the output of the PV
module. The MPPT circuit model is used to evaluate the effect of a feedback loop in the
operation of the PV system.
4.4.1 Validation of PV Model
The PV panel is modeled as described in Section 3.3.2, using the electrical characteristics of the
Sharp NE-80EJEA provided by the manufacturer’s datasheet. The open circuit voltage is 21.6V
while the short circuit current is 5.16A. The maximum power delivered is 80W, and the
maximum power voltage and current occur at 17.3V and 4.63A respectively. The PV module is
initially modeled under varying irradiation conditions with the solar cell temperature set to
25ºC. The I-V characteristic of the solar cell for irradiance values of 600, 800, and 1000 W/ m2
are is shown in Fig. 4.1.
43
Fig 4.1: I-V characteristic at 600, 800, 1000 W/m2 irradiation levels
Operating temperature affects the electrical output of the solar module. The I-V characteristic
with varying operating temperature is shown in Figure 4.2. The module is set to operate with an
irradiance value of 1000 W/ m2. The operating temperatures are set at 20ºC, 25ºC, 40ºC, and
55ºC. The x-axis is the module’s voltage while the y-axis is the module’s current.
Fig 4.2: I-V characteristic at 20ºC, 25ºC, 40ºC, and 55ºC operating temperature
44
It should be noted that the short circuit current of the cell depends linearly on irradiation while
the open circuit voltage depends logarithmically on irradiation. Therefore it would seem that
the output voltage should increase as the irradiation level increases. However this is not
necessarily so, since the cell temperature is likely to rise as the irradiation level increases. As
discussed in chapter 2, an increase in cell temperature will generally lead to a reduction of the
output voltage. This makes it imperative to consider the effect of temperature on the cell output
voltage as illustrated in Fig. 4.2. Overall, there is a reduction of the voltage at higher irradiances
due to the accompanying higher cell temperature [23]. A reduction in the terminal voltage or
current will lead to a decrease in the output power since both the voltage and current are
directly proportional to the output power, IVP ×= . The effect of irradiance and temperature
on the output power of the solar cell is shown in Fig. 4.3 and Fig. 4.4.
Fig 4.3: Output power at 600, 800, 1000 W/m2 irradiation levels
The solar cell terminal voltage is located on the x-axis while the module‘s current and output
power are located on the y-axis.
45
Fig 4.4: Output power at 20ºC, 25ºC, 40ºC, and 55ºC operating temp
The PV model’s I-V characteristic closely matches the I-V characteristic provided in the
manufacturer’s data sheet and shown in Figure 3.5. The effect of decreasing irradiation level is
demonstrated. It mostly affects the module’s current and has only a slight effect on the
module’s voltage. The effect is greater on the module’s current since the current decreases
linearly with decreasing irradiance while the module’s voltage only decrease logarithmically
with decreasing irradiance. It is also observed that an increase in the operating temperature of
the module has a reducing effect on the output voltage. Increasing module temperature causes a
reduction of the output voltage and thus the output power of the solar module. If the
temperature rises too much the cell may also be damaged by ‘hot spots’ [24].
4.4.2 Experimental Data The example solar module was setup in the lab to verify the manufacturer’s data and observe
the effect of irradiance and temperature on the module’s output voltage and current. The
example solar module is shown in Fig. 4.5. The experimental setup involved measuring the
output voltage and current under various illumination conditions.
46
Fig 4.5: Sharp NE-80EJEA solar module used in experiment
The experiment was performed in both indoor and outdoor environments. The outdoors setup
involved taking measurements under bright sunshine, slightly cloudy and very cloudy
conditions. This allows for the observation of the solar module’s response to varying irradiance
levels. The indoor setup involved taking measurements under two artificial lighting conditions.
The artificial lighting was achieved by using the laboratory’s fluorescent lighting and an
incandescent lamp. The different ambient temperature between the outdoor setup and the
indoor setup allows for the observation of the module’s response to varying temperature
conditions. The results are presented in Tables 4.1 and 4.2.
Table 4.1:
Solar module measurements outdoor conditions:
Load
Resistance
(Ω)
Temp.
(°C)
Bright Sunshine
Output Voltage
(V)
Slightly Cloudy
Output Voltage
(V)
Very Cloudy
Output Voltage
(V)
Partial Shadow
Output Voltage
(V)
∞ (Voc) 41.5 19.54 17.81 8.00 18.4
4.9 41.5 18.7 17.44 4.14 13.6
10.5 41 18.6 16.14 7.64 11.2
17 40 18.1 16.06 6.40 14.4
47
Table 4.2:
Solar module measurements under indoor conditions:
Load
Resistance
(Ω)
Temp.
(°C)
Fluorescent Light
Output Voltage
(V)
Incandescent Lamp
Output Voltage
(V)
∞ (Voc) 25 7.83 13.75
As predicted from the PV model derived in chapter 3, the general trend for the solar module
used in the experiment is a decrease in the output voltage and current as the module’s exposure
to the sun is reduced due to the presence of clouds. The output voltage is highest under bright
sunshine and the output decreases under very cloudy conditions to less than half the output
under bright conditions. The difference between the measured open circuit output voltage
(19.54 V) and the manufacturer’s specified open circuit voltage (21.6 V) may be attributed to
the higher module temperature of 41.5 °C in the outdoor environment of our test case. The
effect of partial shadow on the output voltage is also investigated and it is observed that a
partial shadow on any part of the solar module will lead to a reduction of the output voltage.
The experiment was also performed under indoor conditions where the ambient temperature is
25 °C, the same temperature as the manufacturer’s test conditions. The illumination indoors
was significantly less than the illumination outdoors, but the output voltage in both indoor
illumination conditions is higher than the output voltage under very cloudy outdoor conditions.
The much lower indoor module temperature may be responsible for this and it demonstrates
that higher irradiation levels do not necessarily lead to a higher output voltage because of the
accompanying increase in temperature.
48
CHAPTER 5
Validation of MPPT Circuit Operation and Optimization
5.1 Validation of MPPT Circuit Modeling and Operation
The function of the MPPT is to maintain the output voltage of the solar module at it maximum
power point regardless of variations in load demand. The MPPT also includes a second voltage
regulation stage that maintains a steady output regardless of variations in the load demand. The
validation of the MPPT circuit modeling and operation is performed in two stages: first the
MPPT will be simulated with varying solar module output voltage, and then it will be verified
via digital simulation by varying the load conditions.
For the first stage the supply’s output voltage is at the maximum power point voltage of the
solar module which was estimated earlier at 17.3V. For ease of simulation the output voltage of
the solar module is assumed to be discrete DC voltages ranging from the open circuit voltage
(21.6V) to 75% of the open circuit voltage (16V). The simulation results for the first stage of
the MPPT at different input voltages are shown in Figures 5.1, 5.2, 5.3 and 5.4.
Fig 5.1: 1st stage of MPPT operating at 17.3V with PV output at 21V
49
Fig 5.2: 1st stage of MPPT operating at 17.3V with PV output at 20V
Fig 5.3: 1st stage of MPPT operating at 17.3V with PV output at 18V
50
Fig 5.4: 1st stage of MPPT operating at 15.9V with PV output at 16V
As shown in Fig. 5.1 – 5.4, for the first three simulations with the PV output voltage greater
than 17.3V, the MPPT is able to maintain the output at the maximum power point of 17.3V.
However in Figure 5.4, where the PV output voltage is only 16V the MPPT can only sustain an
output voltage equal to the output voltage of the PV module. This is somewhat expected as the
MPPT is of the buck converter type which is only able to output a voltage smaller than the
input voltage. Therefore if the solar output falls below 17V due to temperature or atmospheric
conditions, then the MPPT can only output a voltage equal to the voltage produced by the PV
module.
Under normal operating conditions, with proper illumination, the PV module’s output voltage
is expected to vary only a couple of volts as temperature and irradiation conditions change [25].
Thus, the buck converter should work well for our design under most conditions. A more
complex design of the MPPT implementing either the buck-boost or Cuk converter type [26]
will solve the problem of low PV output voltage as both converter types can either reduce or
increase the output voltage from a nominal input voltage.
51
The second stage of the MPPT is the output voltage regulation stage. The MPPT is able to
maintain a constant charging voltage of 12V to the ultra-capacitor or battery regardless of
changes in load conditions. A simulation of the second stage of the MPPT is shown below in
Fig. 5.5.
Fig 5.5: 2nd stage of MPPT with PV output at 17.3V and MPPT output at 12V
Now to check if the feedback loop can maintain the output voltage at the required 12V in
steady-state that is required to charge the ultra-capacitor and/or battery bank. A transient load is
applied to observe the tracking response of the MPPT against any load variation. The transient
load is achieved by using a pulsed current source to add a 1A increase in load demand between
1.0 ms and 2.0 ms. A second simulation is performed with the pulsed load added between
2.5 ms and 3.5 ms. The results of the simulation are shown in Fig. 5.6 and 5.7, respectively.
From the simulation results of Fig. 5.6 and 5.7, it is observed that the designed MPPT in
Fig. 3.16 is able to quickly adjust the output voltage to the desired output voltage of 12V even
with the increase in load demand.
52
Fig 5.6: MPPT output voltage with pulsed load added between 1.5ms and 2.5ms
Fig 5.7: MPPT output voltage with pulsed load added between 2.5ms and 3.5ms
53
5.2 Control and Optimization using Microcontroller
In coming up with an MPPT design, one of the more important factors that was considered was
the simplicity of the design. The goal was to model a simple MPPT that would effectively
extract the most power from the PV module. The components used are readily available and
the MPPT does not require a complex tracking mechanism. However, to further improve the
control performance and increase the functionalities for general-purposed MRDEG systems, a
low-cost microcontroller is preferred. A microcontroller can replace multiplying analog and
digital components, such as the error amplifier circuit and the PWM circuit.
Most microcontrollers incorporate timers, PWM Input and Output, A/D and D/A interfaces,
Interrupts for timing control and communications. They can also perform comparison
functions. A simple microcontroller, the PIC16F873, has being evaluated and its features which
include 8K x 14 bytes of flash memory, 368 x 8 bytes of RAM, five A/D and two D/A
channels can be used to control a MPPT power circuit and tracking operation. The PIC16F873
offers a good balance of features, low cost and low power consumption. Key specifications and
technical data are given in Appendix B. The use of a microcontroller provides more benefits as
the MPPT operation can be enhanced by implementing a digital control strategy. An effective
digital control strategy will better match the PV module’s output to the maximum power point
when compared to the analog control method [27].
5.3 Feedback Control using Microcontroller
In the case of a practical implementation, a feedback control loop is necessary to ensure proper
operation of the maximum power tracking. The feedback loop is used to continuously adapt the
maximum power point as temperature and load conditions vary. The feedback control also
ensures the stability of the MPPT and prevents unsafe operating conditions of the PV module
and the load. Several methods to control the operation of the MPPT have been proposed [28].
Two of the most widely used control methods are the voltage-feedback control and the power-
feedback control.
54
For the voltage-feedback control, the solar panel terminal voltage is used as the control variable
for the MPPT. This system keeps the solar panel operating close to its maximum power point
by regulating the panel’s voltage and matching the solar panel voltage to the desired voltage.
The advantage of this approach is that no calculations are required in determining the panel’s
operating voltage and a simple op-amp circuit is sufficient to carry out the regulating and
matching functions. However, the voltage-feedback control method has some limitations
including neglecting the effect of temperature and insolation on the solar panel. Hence, this
method is only suitable for use when the effects of insolation and temperature are minimal.
The other commonly used control method is the power-feedback control method. Here, the
maximum power control is achieved by forcing the derivative of the output power against the
terminal voltage ( )dVdP to be equal to zero [29]. The general approach is to measure and
maximize the power at the load terminal by matching the change in power delivered to the
change in output voltage. The advantage of the approach is that the maximum power can be
delivered to the load without necessarily knowing the solar panel characteristics. However, this
approach only maximizes the power delivered to the load and not the power extracted from the
solar panel.
A combination of both the voltage-feedback control and the power- feedback control method
results in a two-dimensional tracking strategy that maximizes the power extracted from the
solar module and the power delivered to the load. To overcome the limitations of the voltage-
feedback control method, wattage sampling techniques [30] are used to continuously find the
solar panel’s optimal operating voltage.
The wattage sampling technique involves periodically introducing a small change in the panel
input voltage, measuring the current, and then calculating the input wattage. If the wattage has
increased over the last sample, then the next change in the reference voltage should continue in
the same direction. The next change in voltage would be in the opposite direction if the wattage
had decreased over the previous sample. This method results in the PV voltage being
dynamically adjusted to increase the output power. While the PV output voltage technically
55
operates close to the actual maximum power point, it oscillates around the true peak point, and
the error should be negligible. A flowchart of the control algorithm for the power-feedback
control is shown in Fig. 5.8.
Fig 5.8: Flowchart of the power-feedback control algorithm
One of the ways of improving the MPPT performance is to optimize the amplitude of the duty
cycle perturbation. Lowering the change in the duty cycle (∆D) reduces the steady-state losses
caused by the oscillation of the solar array operating point around the maximum power point
[31]. However, reducing ∆D makes the algorithm less efficient under certain conditions. A
lower ∆D means the algorithm is unable to quickly adjust to rapidly changing atmospheric
conditions since it has to run through several iterations before arriving at the maximum power
point.
Another parameter that affects the performance of the MPPT is the sampling interval used in
the wattage sampling technique. The sampling interval must be properly set above a threshold
value in order to avoid instability of the MPPT algorithm and to reduce the number of
oscillations around the MPP in steady-state operation. The threshold value for the sampling
interval takes into account the transient behavior of the whole PV system when sampling the
array voltage and current. Thus, after each duty cycle perturbation, the system should reach
steady-state before the next measurement of array voltage and current is performed.
56
5.4 Application of Artificial Neural Networks
Further optimization of the MPPT algorithm can be achieved and implemented by using
artificial neural networks to predict the maximum power point of the solar array [32]. Steady-
state losses are reduced by using smart approximation to predict the location of the maximum
power point which reduces the number of iterations required to reach the MPP and minimizes
the oscillation around the MPP.
Artificial neural networks (ANN) are electronic models based on the neural structure of the
brain. The ANN mimics the function of the brain by ‘learning’ from experience. This function
permits ANNs to be used in the design of adaptive and intelligent systems since they are able
solve problems from previous examples. ANN models involve the creation of massively
paralleled networks composed of mostly of nonlinear elements known as neurons. Each model
involves the training of the paralleled networks to solve specific problems.
The ANN models work by associating an output value to each neuron, known as the neuron’s
activation. A value called the synaptic weight is also associated with each connection between
the neurons. The activation of each neuron then depends on the activations of the neurons
connected to it and the interconnection weights. ANNs are simple clustering of neurons in
layers, where the activations of the input layer are set by an external parameter. Most networks
contain at least three layers – input, hidden, and output. The input layer receives data usually
from an external source while the output layer sends information to an external device. There
may be one of more hidden layers between the input and output layers. Artificial neural
networks are defined by their network topologies, the features of their neurons, and by their
training or learning algorithm [33].
5.4.1 Back-propagation
The most common type of learning algorithm is the back-propagation method. The back-
propagation network is an example of a non-linear layered feed-forward network. The back-
57
propagation network able to adapt by using a learning set consisting of some input examples
and the known-correct output for each case to learn the expected behavior. The learning
process works in small iterative steps as the learning set is applied to the network and the output
produced based on the current synaptic weights is compared to the known-correct output and a
mean-squared error is calculated. The error value is propagated back through the network and
small adjustments are made to the weights in each layer. The process is repeated until the error
value drops below some threshold value. At this point, the network has sufficiently learned the
problem.
The back-propagation type of learning method is suitable for use in predicting the maximum
power point of a solar array [34]. The algorithm is trained by using data collected from the solar
array. The insolation, temperature and load voltage values are used as the activation values for
the input layer of the network. The structure of the proposed back-propagation neural network
is shown in Fig. 5.9. The network is fully connected meaning that the output of each neuron is
connected to all neurons in the hidden layer through the synaptic weight. The weights are
continuously updated through successive iterations until the error drops below the threshold
value [34].
Fig 5.9: Structure of back-propagation neural network for maximum power tracking
58
The back-propagation algorithm is stored on the micro-controller while the insolation,
temperature, and load voltage data are collected for each tracking cycle. The microcontroller
uses the data as the activation input to run the back-propagation algorithm. Once the back-
propagation neural network is trained the algorithm estimates the maximum power point
voltage and current. This operating point is used as the starting position for determining the
maximum power point using the wattage-sampling control method.
The Pseudo-code for the proposed back-propagation algorithm is described below:
• Initialize weight vector W to small random numbers for both layer transition
• Set constants and initialize variables
• Train algorithm by taking input vector and setting to target vector by
setting appropriate learning rate
• Create values at hidden and output nodes
• Create deltas first at the output nodes and then at the hidden nodes
• Update the weights
• Compute the sum-squared error and the average error
• Repeat until termination condition is met
The solar array voltage and current are at the maximum power point when the error is below
the threshold value. An appropriate learning rate is selected by adjusting the change in error and
the array operating point. A gradient descent minimization can be performed on the error
function to smooth the learning rate [35].
59
CHAPTER 6
Conclusion and Future Work
6.1 Conclusion The aim of this research work is to develop a method to optimize the energy extraction from a
proposed renewable energy generation system. In order to achieve this, the components and
subsystems have to be analyzed and validated. The validated models can then be used to
maximize the power output of the conversion system.
The photovoltaic model was modeled and validated in PSpice. The results of the simulation
were compared to experimental data obtained in the lab and both results were found to be very
close. The simulations showed the effects of irradiance and temperature on the operating
condition of the photovoltaic module. The simulation results showed that an increase in
irradiance generally caused an increase in the module’s output current while an increase in
operating temperature generally caused a drop in the module’s terminal voltage. In fact, the
results showed a linear relationship between the short circuit current and the irradiance level
while there is a logarithmic relationship between the open circuit voltage and the operating
temperature.
An MPPT design was implemented and modeled in PSpice. The simulation results of the
MPPT showed that the tracker was able to maintain the operating point of the photovoltaic
module at the maximum power point thereby improving the amount of energy successfully
extracted from the module. The MPPT also performed well as a charge regulator to the energy
storage components.
The simulation results indicate that a significant amount of additional energy can be extracted
from a photovoltaic array by using simple analog or digital maximum power point trackers.
This results in improved efficiency for the operation of renewable energy generation systems.
The improved efficiency should lead to significant cost savings in the long run.
60
6.2 Further Work In the future, a more detailed model of the photovoltaic module can be developed from the one
presented in this work. The more detailed model may take into account the effect of shading or
partial shadows on the operation of the module. Also the effects of scaling up the photovoltaic
sources may be investigated to determine the suitability for large scale deployment.
Different algorithms for maximum power control can be developed for application on other
renewable energy sources such as fuel cells and wind power. Artificial neural network
algorithms can be developed to improve the performance of the solar energy conversion
function of the MPPT. Overall, the shift from conventional energy sources to alternative energy
means a lot more work needs to be done to fulfill the desire to produce clean, affordable and
sustainable energy.
61
APPENDIX A (Components and Subsystems)
Figure A-1: MPPT Circuit PSpice Schematic
62
Figure A-2: Experimental setup for solar module under indoor conditions
63
Figure A-3: Sharp NE-80EJEA Solar Cell Data Sheet
64
Figure A-4: IdaTech FCS 1200 Fuel Cell Data Sheet
65
Figure A-5: Maxwell BOOSTCAP Ultracapacitor Data Sheet
66
Figure A-5(b): Maxwell BOOSTCAP Ultracapacitor Data Sheet
67
APPENDIX B (Microcontroller)
Figure B-1: Microchip PIC16F873 Microcontroller Data Sheet
68
Figure B-2(b): Microchip PIC16F873 Microcontroller Data Sheet
69
Figure B-3(c): Microchip PIC16F873 Microcontroller Data Sheet
70
APPENDIX C (Power MOSFET)
Figure C-1: Intersil IRF150 Power MOSFET Data Sheet
71
Figure C-1(b): Intersil IRF150 Power MOSFET Data Sheet
72
Figure C-1(c): Intersil IRF150 Power MOSFET Data Sheet
73
Figure C-1(d): Intersil IRF150 Power MOSFET Data Sheet
74
Figure C-1(e): Intersil IRF150 Power MOSFET Data Sheet
75
APPENDIX D (Schottky Diode)
Figure D-1: Fairchild Semiconductor MBR0520L Schottky Diode Data Sheet
76
Figure D-2: Fairchild Semiconductor MBR0520L Schottky Diode Data Sheet
77
APPENDIX E (Current Sensor)
Figure E-1: LEM LA-10PB Current Sensor Data Sheet
78
Figure E-1(b): LEM LA-10PB Current Sensor Data Sheet
79
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BIOGRAPHICAL SKETCH Adedamola Omole was born and raised in Ile-Ife, Osun State, Nigeria. He attended high
school at Federal Government College, Odogbolu and obtained his B.S. degree in
Electrical Engineering from Florida State University in 2004. He joined the M.S.
program at FSU in 2004 and worked under the supervision of Dr. Jie Chang at the Center
for Advanced Power System (CAPS). Damola is a member of IEEE and his area of
interest include power and communication systems.
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